All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Mission impossible (Posted on 2013-04-03) Difficulty: 2 of 5
In a certain football contest the winner scores 3 points, the loser 0, and in the case of a draw each team scores 1 point.

Out of all "possible" final scores (0<R<3*n) for a team, participating in N games, how many final results cannot be achieved?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Not achieved (spoiler) | Comment 1 of 5
(I want to say the answer is zero since if a score cannot be achieved it is not possible.  But I know this isn't what you mean.   I don't remember this problem from the queue or I'd have suggested a rewrite.)

The answer is 1.  For N games the only unachievable score is 3N-1.

Numbers of the form 3m can be (W,L,D) = (m,N-m,0)
Numbers of the form 3m+1 can be (m,N-m-1,1)
Numbers of the form 3m+2 can be (m,N-m-2,2) except where
there is only 1 non-win.  In that case there cannot be 2 draws.

  Posted by Jer on 2013-04-03 11:32:42
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information